Relative Velocity Part 4  In this packet we look at how to determine the relative velocity of two objects when the objects are moving at angles to one another.  This packet includes a video giving a detailed solution of how to find the velocity of a car relative to an airplane while the airplane is taking off.  The video will go over: How to set-up the problem How to solve the problem How to interpret the solution  To fully understand the solution I highly recommend that the student have a good understanding of Pythagorean Theorem and the basic Trigonometric Functions (Sin-Cos-Tan).

Things To Pay Attention For In this video pay attention to how you can set-up the relative velocity equation: In particular pay attention to how I relate p, A, and B to terms that better describe the problem and why I decide to start with writing the velocity of the car with respect to the ground, v c/g, first. The student should understand why we can write the velocity vectors with respect to the ground before anything else. (Hint: Writing velocity vectors with respect to the ground is what we normally write when describing the velocity of an object. In this case we are just being more precise.) That is to say:

Pay attention to why I had to break the velocity vectors of the car and the airplane into their x-components and y-components. (Hint: You can only add vectors that are moving in the same axis.) Once I broke the vectors into their component parts, try to understand why and how I reassembled the vector. (Hint: When we talk about vectors, by definition, they must have a magnitude and direction. Whether that direction be North, South, East, West or anywhere in between or at an angle from the horizontal of an object we are relating the vector to or from.)

Some Review θ Hypotenuse (h) Adjacent (a) Opposite (o) The length (or in vector terms, magnitude) of the adjacent and opposite sides of this right triangle can be written as the following: This follows from the equations to the left after some algebraic manipulation. This is also the underlying reason why in the video I was able to break the velocities of the car and airplane into their component parts. I was able to combine them again using: Pythagorean Theorem: